{"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00224844","sets":["1164:6389:11170:11171"]},"path":["11171"],"owner":"44499","recid":"224844","title":["Module-LWEからRing-LWEに帰着できる代数体の範囲の拡大"],"pubdate":{"attribute_name":"公開日","attribute_value":"2023-03-06"},"_buckets":{"deposit":"1abd643a-d241-43bc-aff8-4b20485612f4"},"_deposit":{"id":"224844","pid":{"type":"depid","value":"224844","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"Module-LWEからRing-LWEに帰着できる代数体の範囲の拡大","author_link":["593849","593850","593846","593848","593851","593847"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Module-LWEからRing-LWEに帰着できる代数体の範囲の拡大"},{"subitem_title":"Expanding Underlying Number Fields Reducing from Module-LWE to Ring-LWE","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"ICSS","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2023-03-06","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"大阪大学工学部"},{"subitem_text_value":"大阪大学工学部"},{"subitem_text_value":"大阪大学工学部"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Faculty of Engineering, Osaka University","subitem_text_language":"en"},{"subitem_text_value":"Faculty of Engineering, Osaka University","subitem_text_language":"en"},{"subitem_text_value":"Faculty of Engineering, Osaka University","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/224844/files/IPSJ-SPT23050030.pdf","label":"IPSJ-SPT23050030.pdf"},"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-SPT23050030.pdf","filesize":[{"value":"1.1 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"0","billingrole":"46"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_login","version_id":"71e0614d-32bd-4241-b6aa-47a754696c64","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2023 by the Institute of Electronics, Information and Communication Engineers This SIG report is only available to those in membership of the SIG."}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"舩津, 颯介"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"宮地, 充子"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"奥村, 伸也"}],"nameIdentifiers":[{}]}]},"item_4_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Sosuke, Funatsu","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Atsuko, Miyaji","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Shinya, Okumura","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA12628305","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8671","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"耐量子計算機暗号において，Learning with Errors（LWE）問題や Ring-LWE（RLWE）問題に関する研究がある．LWE 問題の困難性に基づく暗号は耐量子計算機暗号であり，かつ準同型暗号などの高機能な暗号を構成できることから注目されている．RLWE 問題は，LWE 問題と比べて送信する鍵のサイズを減らすことが可能な環上の LWE 問題であり，特に 2 冪の円分環において効率的である．そして RLWE 問題に階数を設定したものがModule-LWE （MLWE）問題である．MLWE 問題はさらに複雑な代数的構造を持っており，RLWE 問題よりも安全性に優れ，LWE 問題よりも性能的に優れている可能性がある．そのため，RLWE 問題と MLWE 問題の困難性を比較するために，MLWE 問題から RLWE 問題へ帰着する手法が提案されている．これまで，2 冪の円分体において探索 MLWE 問題から探索 RLWE 問題に帰着できることが証明された．また，任意の円分体において識別 MLWE 問題から識別 RLWE 問題に帰着できることが示された．そこで本研究では，円分体のほかに MLWE 問題から RLWE 問題に帰着できる代数体を探すことを目的とする．結果，素数 ???? に対して，???? 次の円分体の部分体の一つである分解体において，識別 MLWE 問題から探索 RLWE 問題への帰着について議論する．","subitem_description_type":"Other"}]},"item_4_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"We have researched Learning with Errors(LWE) problem and Ring-LWE problem in post-quantum cryptography. The RLWE problem is an LWE problem over rings that can reduce the size of keys to be sent compared to the LWE problem, and is particularly efficient in power-of-two cyclotomic rings. Module-LWE problem is a variant of RLWE problem with module rank. We can compare the hardness of RLWE problem and MLWE problem by reducing MLWE problem to RLWE problem. So far, it has been proved that MLWE problem can be reduced to RLWE problem in cyclotomic fields. Thus, the purpose of this study is to search for number fields other than cyclotomic fields that can be reduced MLWE problem to RLWE problem. As a result, for a prime number ????, we discuss a reduction from the dicision MLWE problem to the search RLWE problem in a decomposition fields which is one of the subfield of a ????-th cyclotomic fields.","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"6","bibliographic_titles":[{"bibliographic_title":"研究報告セキュリティ心理学とトラスト（SPT）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2023-03-06","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"30","bibliographicVolumeNumber":"2023-SPT-50"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":224844,"updated":"2025-01-19T13:00:04.254022+00:00","links":{},"created":"2025-01-19T01:24:24.342158+00:00"}